Question

Assume that y varies inversely with x. If y=1/3 when x=1/2, find y when x=1/4.

Answer 1

Answer:

y = $\frac{2}{3}$

Step-by-step explanation:

Given that y varies inversely with x then the equation relating them is

y = $\frac{k}{x}$ ← k is the constant of variation

To find k use the condition y = $\frac{1}{3}$ when x = $\frac{1}{2}$ , thus

$\frac{1}{3}$ = $\frac{k}{\frac{1}{2} }$ = 2k ( divide both sides by 2 )

k = $\frac{1}{6}$

y = $\frac{1}{6x}$ ← equation of variation

When x = $\frac{1}{4}$ , then

y = $\frac{1}{6(\frac{1}{4}) }$ = $\frac{1}{\frac{3}{2} }$ = $\frac{2}{3}$